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Master Variable Equations: Rules, Examples, and Solutions

Dive into the world of variable equations with this guide on solving one-step linear equations step by step, from understanding the basics to mastering the rules for isolating variables. Practice various equation examples to boost your problem-solving skills. Explore the concepts of balancing equations and apply the rules effectively to find solutions. Simplify and reduce all answers to navigate through equations involving fractions easily. Level up your math skills and solve equations with confidence!

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Master Variable Equations: Rules, Examples, and Solutions

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  1. Objective - To solve simple, one-step variable equations What is an equation? Equation - a balanced statement of equality between two quantities. 4 + 3 = 7 4 + 3 7 = fulcrum

  2. Rules for Solving Linear Equations 1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation.

  3. Solve. 1) m + 2 = 10 4) m - 4 = 9 -2 -2 +4 +4 m = 8 m = 13 5) 11 = x - -2 2) x - 4 = 6 +4 +4 -2 -2 x = 10 9 = x 3) x + 7 = 3 6) 8 + y = -6 -7 -7 -8 -8 x = -4 y = -14

  4. Solve. 1) -4 + x = 15 4) - 4 = m + 9 +4 +4 -9 -9 x = 19 -13 = m 2) 7 = x + 13 5) 9 + 7 = x -13 -13 16 = x -6 = x 3) -10 = 6 + x 6) y = 8 - 13 -6 -6 y = -5 -16 = x

  5. Solve. 1) 5x = 35 3) 9 = -3m -3 -3 5 5 -3 = m x = 7 2) 4) (-6) (-6) -72 = x

  6. Acceptable Answers -4k = 14 -4 -4 All answers must be fully reduced! There is nothing improper about an improper fraction!

  7. Solve. 1) 7x = 16 3) 9 = -m 7 7 9/(-1) = -m/(-1) -9 = m 2) 4) (-4) (-4) (-2) (-2) k = 16

  8. Solving Equations Involving Fractions Long Way Short Way Easier to multiply by the reciprocal!

  9. Solve. 1) 3) 2) 4)

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